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Interaction

Sukon Kanchanaraksa, PhDJohns Hopkins University

3

What Is (Biological) Interaction?

Interaction involves two risk factors (and their effect on one disease outcome)If the effect of one risk factor is the same within strata defined by the other, then there is NO interactionWhen the effect of one risk factor is different within strata defined by the other, then there is an interaction (biological)

4

Example of (Biological) Interaction

Cigarette smoking and radon exposure are two possible risk factors for lung cancer−

Is there an interaction (biological) between cigarette smoking and radon exposure with regard to lung cancer?

−

If the risk of lung cancer from cigarette smoking is the same among those who were exposed to radon and those who were not exposed to radon, then there is no interaction (biological) between the two risk factors

−

If the risk differs in the two groups, then there is an interaction

How do we measure or check for the presence/absence of an interaction?

5

Measures of Interaction

There are two ways that we measure risk1.

Ratio of risks

2.

Difference of risks

(Statistical) interaction can be measured based on the ways that risks are calculated (modeling)−

When ratio is used, risks are considered to act in a multiplicative way

−

When difference is used, risks are considered to act in an additive way

The presence of interaction based on measurements is called statistical interaction, and inherently it may not reflect the true biological interaction

6

(Statistical) Interaction or Effect Measure Modification

(Statistical) interaction occurs when the incidence of disease in the presence of two or more risk factors differs from the incidence expected to result from their individual effects

Source: MacMahon, 1972

7

Implications of Interaction

Synergism increases disease risk beyond expected; persons with one exposure (smoking) are more susceptible to another exposure (radon)Antagonism decreases disease risk beyond expected; persons with one exposure (smoking) are less susceptible to another (radon)

8

Incidence Factor A

– +

Factor B– 3 9

+ 15 ?

Hypothetical Data in an Additive Model

9

Risk Difference (Attributable

Risk)Factor A

– +

Factor B– 0 6

+ 12 ?

Subtracting Baseline Risk from Each Category

Incidence Factor A

– +

Factor B– 3 9

+ 15 ?

10

?+ =

A B A+B

Incidence

What Is the Expected Incidence of A+B in an Additive Model?

11

What Is the Expected Incidence of A+B in an Additive Model?

Baseline

A A+BB

+ =Incidence

12

?+ =

A B A+B

What Is the Expected Incidence of A+B in an Additive Model?

9 15

Baseline3

9

3

6

3

12

15

3

6

12

21

13

Expected Incidence in an Additive Model

Expected incidence of A and B = Attributable risk of A alone

+ attributable risk of B alone

+ baseline

= Incidence of A alone

+ incidence of B alone –

baseline

Expected incidence of A and B = Attributable risk of A alone

+ attributable risk of B alone

+ baseline

= Incidence of A alone

+ incidence of B alone –

baseline

14

Incidence Factor A

– +

Factor B– 3 9

+ 15 21

Hypothetical Data in an Additive Model

If there is no interaction between Factors A and B, the incidence of having A and B is expected to be 21If the observed incidence in the group having A and B differsfrom 21, then there is an interaction (statistical) under the additive model

15

Test for the Presence/Absence of Interaction

No interaction: I11 – I01 = I10 – I00

Synergistic interaction: I11 – I01 > I10 – I00

Antagonistic interaction: I11 – I01 < I10 – I00

Incidence Factor A

– +

Factor B– I00 I10

+ I01 I11

16

Smoking RadonLung Cancer

Incidence

No No 1/1000

No Yes 5/1000

Yes No 10/1000

Yes Yes 50/1000

Smoking and Radon Exposure In Uranium Miners

17

Smoking and Radon Exposure in Uranium Miners

Incidence Smoking

– +

Radon– 1 10

+ 5 50

If there is no interaction between smoking and radon exposure, the incidence of having both is expected to be:

(5–1)+(10–1) +1 = 14 (or, 5 + 10 –1 = 14)

But observed incidence is 50/1000; therefore, there is a synergistic interaction in the additive model

18

Using the Test Equations

I11 - I01 > I10 - I00

50 - 5 > 10 - 1

Suggests synergistic interaction

Incidence Smoking

– +

Radon– 1 10

+ 5 50

19

Incidence Factor A

– +

Factor B– 3 9

+ 15 ?

Same Hypothetical Data in a Multiplicative Model

20

Relative Risk Factor A

– +

Factor B– 1.0 3.0

+ 5.0 ?

Calculating Ratio of Risk or Relative Risk in a Multiplicative Model

Dividing by baseline incidence of 3

Incidence Factor A

– +

Factor B– 3 9

+ 15 ?

21

Expected RR for A+B = RR for A only x RR for B onlyExpected RR for A+B = RR for A only x RR for B only

Expected Relative Risk for A+B in a Multiplicative Model

22

Relative Risk Factor A

– +

Factor B– 1.0 3.0

+ 5.0 ?

The Expected RR for Having Factors A and B in a Multiplicative Model

The expected RR for having both A and B = 3.0 x 5.0 = 15.0

The incidence of having both A and B = baseline I x RR= 3 x 15.0 = 45

15.0

23

Types of Interaction

If the observed risk (or incidence) for having both A and Bis equal to the expected, then there is no interactionIf the observed risk (or incidence) for having both A and B is greater than the expected risk (or incidence), then there is a synergistic interactionIf the observed risk (or incidence) for having both A and B is less than the expected risk (or incidence), then there is an antagonistic interaction

24

Test for the Presence/Absence of Interaction in a Multiplicative Model

Relative Risk Factor A

– +

Factor B– RR00 RR10

+ RR01 RR11

No interaction : RR11 = RR10 x RR01

Synergistic Interaction : RR11 > RR10 x RR01

Antagonistic interaction : RR11 < RR10 x RR01

25

Example: Relative Risk of Oral Cancer from Smoking and Alcohol Consumption

Relative Risk Smoking

No Yes

Alcohol Consumption

No 1.00 1.53

Yes 1.23 5.71

Rothman K, Keller A. (1972). The effect of joint exposure to alcohol and tobacco on risk of cancer of the mouth and pharynx. J Chronic Dis

25:711-716.

26

Example: Relative Risk of Oral Cancer From Smoking and Alcohol Consumption

Relative Risk Smoking

No Yes

AlcoholNo 1.00 1.53

Yes 1.23 5.71

1.

The expected RR for smoking and drinking alcohol

= 1.53 x 1.23 = 1.882.

Using the test equation to check for interaction

5.71 > 1.53 x 1.23

Suggest synergistic interaction in the multiplicative model

27

Use of Relative Risk in an Additive Model

1. Incidence Factor A

– +

Factor B– 3 9

+ 15 21

2. Attributable Risk

Factor A

– +

Factor B– 0 6

+ 12 18

3. Relative Risk Factor A

– +

Factor B– 1.0 3.0

+ 5.0 7.0

28

Use of Relative Risk in an Additive Model

1. Incidence Factor A

– +

Factor B– 3 9

+ 15 21

2. Attributable Risk

Factor A

– +

Factor B– 0 6

+ 12 18

3. Relative Risk Factor A

– +

Factor B– 1.0 3.0

+ 5.0 7.0

No interaction :

(1) I11- I01 = I10 - I00

No interaction :

(2) RR11 - RR01 = RR10 - RR00

(3) RR11 - RR01 = RR10 - 1

(4) RR11 = RR01 + RR10 - 1

29

Example of Interaction

Effect of aflatoxin in chronic hepatitis B patient on the development of liver cancer−

RR of liver cancer from hepatitis B infection alone was 7.3

−

RR of liver cancer from aflatoxin exposure alone was 3.4−

RR of liver cancer from both was 59.4

Qian GS, Ross RK, Yu MC, et al. (1994). A follow-up study of urinary markers of aflatoxin

exposure and liver cancer risk in Shanghai, People’s Republic of China. Cancer Epidemiol Biomarkers Prev

3:3-10.

30

Statistical Interaction versus Biological Interaction

Is the presence of a biological interaction between two risk factors based on the expectation that the risk factors should interact following an additive or a multiplicative model? Or, should it be based on a special law of biology that is more complex than the measurement tools (modeling) available? The answer will likely require a better understanding of the underlying biological mechanisms of disease causation and the causal (or risk) factorsSince several factors play a role in disease causation, it is important to understand the concept of interaction—especially in individuals with multiple risk factors